No, if your boyfriend is claiming the children on his tax return you cannot claim the Child and Dependent Care Credit. When parents live together only one parent may claim the child(ren) for all benefits. Since your boyfriend is claiming the children he may claim the Child and Dependent Care Credit if he qualifies.
Note: When parents are divorced, separated, or live apart, there is a special rule that lets the custodial parent give permission to the noncustodial parent to claim the child as a dependent and for the Child Tax Credit.